John C wrote in part:
|
| Consider that less than 10% of HS graduates can apply formal
| logic according to a paper by Lawson et al. This means that
| students will have great difficulty really understanding
| proof. Now it is possible to get them to do proof, but it is
| not possible to do it by most of the conventional methods.
| Consider that the majority of middle school children are
| concrete operational so that the conventional methods of
| teaching algebra are doomed to failure. This means they are
| incapable of hypothetico-deductive logic, but they can use
| empirical inductive logic. Actually only about 20% of HS
| graduates are fully able to use hypothetico-deductive
| deductive logic and some are able to use it part of the time.
|
How does one push a student from piagetian level to the next. I suspect
that one has to do tasks that are above the level that the student is
currently occupying. (gently and patiently of course)
Meaning even if only 10% of high school students can do a proof; it
probably is a good idea to introduce them to the idea of a proof.